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I live in the northern foothills of the Catskill Mountains in New York State, USA. We have a small, steep sunny slope (that is man-made) overlooking our backyard. The slope is rock underneath with a thin layer of soil over the top. What sorts of herbs would grow well in a spot like this where it will be dry and there is little soil (which we hope whatever we grow will help keep the soil there)? Grass is so boring.

You could try wild thyme, creeping thyme or rupturewort. You would probably have a better chance to establish the plants if you start with plugs or plants. With direct seeding you may have troubles because the thin layer of soil will make it hard to keep the soil evenly moist until the seedlings are established.